MinT - Best Known (163−69, 163, s)-Nets in Base 4

Best Known (163−69, 163, s)-Nets in Base 4

(163−69, 163, 130)-Net over F₄ — Constructive and digital

Digital (94, 163, 130)-net over F₄, using

13 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(163−69, 163, 204)-Net over F₄ — Digital

Digital (94, 163, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−69, 163, 3306)-Net in Base 4 — Upper bound on s

There is no (94, 163, 3307)-net in base 4, because

1 times m-reduction [i] would yield (94, 162, 3307)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 362550 668779 051306 716850 795168 998801 341105 375941 642030 614867 799270 154119 783116 716396 686978 964715 > 4¹⁶² [i]